Abstract
A new time-frequency representation called Dopplerlet transform, which uses the dilated, translated and modulated windowed Doppler signals as its basis functions, is proposed, and the Fourier transform, short-time Fourier transform (including Gabor transform), wavelet transform, and chirplet transform are formulated in one framework of Dopplerlet transform accordingly. It is proved that the matching pursuits based on Dopplerlet basis functions are convergent, and that the energy of residual signals yielded in the decomposition process decays exponentially. Simulation results show that the matching pursuits with Dopplerlet basis functions can characterize compactly a nonstationary signal.
Similar content being viewed by others
References
S. E. Qian, D. P. Chen, Signal representation via adaptive normalized Gaussian functions. IEEE Trans. on Signal Processing, 36(1988)1, 1–11.
S. G. Mallat, Z. F. Zhang, Matching pursuits with time-frequency dictionaries. IEEE Trans. on Signal Processing, 41(1993)12, 3397–3415.
S. Mann, S. Haykin, The chirplet transform: Physical considerations. IEEE Trans. on Signal Processing, 43(1995)11, 2745–2761.
D. Mihovilovic, R. N. Bracewell, Whistler analysis in the time-frequency plane using chirplets. J. Geophys. Res., 97(1992)A11, 17199–17204.
Author information
Authors and Affiliations
Additional information
Supported by the National Natural Science Fundation of China (Grant No.69775009)
About this article
Cite this article
Zou, H., Zhou, X., Dai, Q. et al. Dopplerlet based time-frequency representation via matching pursuits. J. of Electron.(China) 18, 217–227 (2001). https://doi.org/10.1007/s11767-001-0031-6
Issue Date:
DOI: https://doi.org/10.1007/s11767-001-0031-6